Weighted G1-Multi-Degree Reduction of B´ezier Curves

In this paper, weighted G1-multi-degree reduction of B´ezier curves is considered. The degree reduction of a given B´ezier curve of degree n is used to write it as a B´ezier curve of degree m,m < n. Exact degree reduction is not possible, and, therefore, approximation methods are used. The weight function w(t) = 2t(1 - t), t [0, 1] is used with the L2-norm in multidegree reduction with G1-continuity at the end points of the curve. Since we consider boundary conditions this weight function improves approximation in the middle of the curve. Numerical results and comparisons show that the proposed method produces fewer errors and outperform all existing methods.

@article{Rababah2016,
  title     = {Weighted G1-Multi-Degree Reduction of B´ezier Curves},
  journal   = {International Journal of Advanced Computer Science and Applications},
  volume    = {7},
  number    = {2},
  year      = {2016},
  publisher = {The Science and Information Organization},
  author    = {Abedallah Rababah and Salisu Ibrahim},
  doi       = {10.14569/IJACSA.2016.070270},
  url       = {https://doi.org/10.14569/IJACSA.2016.070270}
}